On the inverse optimum control problem for a class of nonlinear autonomous systems

Author

Thau, Fred E.

Author_Institution

General Precision, Incorporated, Little Falls, NJ, USA

Volume

12

Issue

6

fYear

1967

fDate

12/1/1967 12:00:00 AM

Firstpage

674

Lastpage

681

Abstract

Some aspects of the inverse optimum control problem are considered for a class of nonlinear autonomous systems. A closed-loop system with a known control law is given; the problem is to determine performance criteria for which the given control law is optimum. Algebraic conditions that must be satisfied by a class of scalar performance criteria of the form $V=\\int\\min{t}\\max {\\infty }[q(x)+h(u)]d_{\\tau }$ are obtained. It is shown that if the value of the optimum V⁰is required to be a quadratic form $V^{o} = frac{1}{2}x\´Mx$ of the current state $x$ , and if certain state variables cannot be measured, then $M$ cannot be positive definite. The inverse optimum control problem corresponding to the problem of Lur\´e is considered. Examples are given to illustrate the techniques and to compare the properties of a linear and nonlinear system having the same optimum performance $V^{0}(x)$ .

Keywords

Inverse optimal control problem; Nonlinear systems; Optimal control; Aerodynamics; Control systems; Control theory; Current measurement; Inverse problems; Kalman filters; Linear systems; Nonlinear control systems; Nonlinear systems; Optimal control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1967.1098741

Filename

1098741